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Algebra Seminar: Lattices and Finite Commutative Groups
1:10 pm, Neill Hall 106W
Abstract: A lattice is the set of all integer linear combinations of a set of vectors. I will talk about lattices, full-rank sub-lattices, and the analysis of the equivalence classes of vectors in a lattice defined by a sub-lattice using basic group theoretic techniques. One of the key operations in working with lattices for cryptography applications is to find "good" representatives for each such equivalence class. I will demonstrate the use of the Hermite Normal Form (HNF) of the matrices associated with the lattices to find such representative elements.